Is there an approach to solve the following radical equation in $$x$$?
$$(P - 1)x = QR\left( Q + \sigma \sqrt{Q^2 + x} \right)\left( R + sign(P-1) \sigma \sqrt{R^2 + x} \right)$$
We know $$x\in (0,1)$$. We also have $$P, Q, R > 0$$ and $$\sigma \in \{-1,+1\}$$.